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. Find the inverse of the function below on the given interval and write it in the form yequalsf Superscript negative 1 Baseline (x ). b. Verify the relationships f (f Superscript negative 1 Baseline (x ))equalsx and f Superscript negative 1 Baseline (f (x ))equalsx.

User Marivel
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1 Answer

6 votes

Answer:

The inverse of the function is
f^(-1)(x)=(x-5)/(3).

Explanation:

The function provided is:


f (x)=3x+5

Let
f(x)=y.

Then the value of x is:


y=3x+5\\\\3x=y-5\\\\x=(y-5)/(3)

For the inverse of the function,
x\rightarrow y.


f^(-1)(x)=(x-5)/(3)

Compute the value of
f[f^(-1)(x)] as follows:


f[f^(-1)(x)]=f[(x-5)/(3)]


=3[(x-5)/(3)]+5\\\\=x-5+5\\\\=x

Hence proved that
f[f^(-1)(x)]=x.

Compute the value of
f^(-1)[f(x)] as follows:


f^(-1)[f(x)]=f^(-1)[3x+5]


=((3x+5)-5)/(3)\\\\=(3x+5-5)/(3)\\\\=x

Hence proved that
f^(-1)[f(x)]=x.

User Kevinarpe
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